ar X iv : n uc l - th / 0 10 50 41 v 1 1 7 M ay 2 00 1 Statistical models of nuclear level densities

We present calculations of nuclear level densities that are based upon the detailed microphysics of the interacting shell model yet are also computationally tractable. To do this, we combine in a novel fashion several previously disparate ideas from statistical spectroscopy, namely partitioning of the model space into subspaces, analytic calculations of moments up to fourth order directly from the two-body interaction, and Zuker’s binomial distribution. We get excellent agreement with full scale interacting shell model calculations. We also calculate “ab initio” the level densities for Si and Co and get reasonable agreement with experiment. PACS:21.10.-k, 21.10.Ma , 26.50.+x Typeset using REVTEX 1 Reliable nuclear level densities are important for the theoretical estimates of nuclear reaction rates in nucleosynthesis [1]. The neutron-capture cross sections are approximately proportional to the corresponding level densities around the nuclear resonance region. The competition between neutron-capture and β decay determines the fate of the s and r processes. Level densities can be extracted experimentally [2], but reaction network calculations require cross-sections for hundreds or thousands of nuclides, many of them short-lived. The most widely used description of the nuclear level density is the Bethe formula, based on a gas of free nucleon [3], and the modified “backshifted Bethe formula” [4]. Despite its ubiquity the Bethe formula is a phenomenological fit often requiring energy dependent parameters to match experimental data. The interacting shell model and other microscopic models accurately describe spectra and transition for a broad range of nuclides. On the other hand, “traditional” shell-model codes diagonalize the Hamiltonian in a large-dimensioned basis of occupation-state wavefunction but use the Lanczos algorithm to extract only a handful low-lying states. The level density requires complete diagonalization, a computationally forbidding requirement. An alternative to diagonalization is the Monte Carlo path-integral technique [5], which is well suited to thermal observables [6,7]. Although reasonably successful, path-integral methods are limited to interactions that are free of the ‘sign problem’ and are still very computationally intensive (i.e., require supercomputer time). Therefore we feel motivated to consider further alternatives. In this Letter we combine several previously disparate ideas based in nuclear statistical spectroscopy: (1) Analytic calculation of moments up to and including fourth-order; (2) partitioning the model space into subspaces; and (3) using binomial rather than Gaussian distributions. We find this combination to be successful, which we demonstate not only against exact shell-model calculations but also against experimental data. Nuclear statistical spectroscopy argues that many nuclear properties are controlled by low-lying moments of the Hamiltonian [8,9]. The first moment (centroid) is H̄ = μ1 = 〈